Due to spatial localization of electron cyclotron wave injection in DIII-D, electrons heated in an off-axis region must toroidally transit the tokamak 25--50 times before re-entering the heating region. This distance is of the order of the mean free path. The effect of such RF localization is simulated with a time-dependent Fokker-Planck code which is 2D-in-velocity, 1D-in-space-along-B, and periodic in space. An effective parallel electric field arises to maintain continuity of the driven current. Somewhat surprisingly, the localized current drive efficiency remains equal to that for a uniform medium

Harvey, R.W.

Lin-Liu, Y.R.

Luce, T.C.

Prater, R.

Sauter, O.

Smirnov, A.P.

UNT Digital Library

GA423137 CURRENT DRIVE DUE TO LOCALIZED ELECTRON POWER DEPOSITION IN DIII-D bY R.W. HARVEY, Y.R. LIN-LIU, Om SAUTER, A.P. SMIRNOV, TIC. LUCE, and R. PRATER MAY 1999 GENE-L ATOMICS DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. DISCLAIMER Portions of this document may be illegible in electronic image products. images are produced from the best available original document. GA-A23137 CURRENT DRIVE DUE TO LOCALIZED ELECTRON POWER DEPOSITION IN DIII-D by R.W. HARVEY,’ Y.R. LIN-LIU, 0. SAUTER: A.P. SMIRNOV,3 T.C. LUCE, and R. PRATER This is a preprint of a paper presented at the 13th Topical Conference on Applications of Radio Frequency Power to Plasmas, April 12-14, 1999, Annapolis, Maryland, and to be printed in the Proceedings. Work supported by U.S. Department of Energy Contract DE-AC03-99ER54463 and in part by the Swiss National Science Foundation lCompX, Del Mar, California 2CRPP/EPFL, Lausanne, Switzerland  MOSCOW State University, Moscow, Russia GENERAL ATOMICS PROJECT 30033 MAY 1999 GENERAL ATOMICS Harvey et al. CURRENTDRNEDUETOLOCALEED ELECTRON CYCLOTRON POWER DEPOSITION IN Dm-D Current Drive Due to Localized Electron Cyclotron Power Deposition in DIII-D R.W. Harvey,’ Y.R. Lin-Liu, 0. Sauter,2 A.P. Srnirn~v,~ T.C. Luce, and R. Prater General Atomics, P. 0. Box 85608, San Diego, California 92186-5608 ’CompX, 12839 Via Grimaldi, Del Mar, California 92014 2CRPP, Ecole Polytechnique Fidkrale de Lausanne, 1007 Lausanne, Switzerland 3Moscow State University, 119899 Moscow, Leninsky Gory, Russia Abstract. Due to spatial localization of electron cyclotron wave injection in DIII-D, electrons heated in an off-axis region must toroidally transit the tokamak 25-50 times before re-entering the heating region. This distance is of the order of the mean free path. The effect of such RF localization is simulated with a time-dependent Fokker-Planck code which is 2D-in-velocity, 1D-in-space-along-B, and periodic in space. An effective parallel electric field arises to maintain continuity of the driven current.Somewhat suprisingly, the localized current drive efficiency remains equal to that for a uniform medium. Electron cylotron ray paths from the launcher in DIII-D typically interceptabout two percent of the poloidal circumference of a flux surface at half the minor radius. Thus, for a typical non-rational value for the safety factor q , it is expected that after an electron is accelerated by the electron cyclotron (EC) in the “heating spot,” it will make an average of 50 turns around the torus before re-entering the heating spot. This connection distance is approximately equal to the mean free path for thermal electrons, equal to 30 toroidal turns for Te = 1.2 keV, ne = 1.7 x cm-3. Electron cyclotron current driven in the EC spot in an off-axis flux surface will collisionally slow down in the resulting current channel; an effective electric field arises maintaining current continuity in the channel. This picture is quite different from the usual toroidally symmetric, bounce-averaged calculation of electron cyclotron current drive (ECCD) (e.g., by CQL3D, [l]). The motivation for this study is recent experimental results by Luce et al. [2] which found agreement between the DIII-D experiment and detailed Fokker-Planck calculations of ECCD for on-axis cases, and substantially higher experimental results than theory for off-axis ECCD. The present work examines the effect of the localized EC spot size on the ECCD efficiency, but does not include the effect of variation of the magnetic field strength following the magnetic field line. A preliminary study [3] has examined collis- ional reduction of the toroidal trapping, and finds that this is a small effect on ECCD efficiency for DIII-D parameters. The Fokker-Planck equation solved for electrons in this study is GENERAL ATOMICS REPORT GA-A23137 1 CuRRENTDFWEDUETOLOCAuzED ELECTRON CYCLOTRON POWER DEPOSlTION Ih' DEI-D -4.10-15' . . . I . . . I . . . I . . . . . . . Harvey et al. C is the full non-linear collision operator f4] except that the PO term in the Legendre expansion for the electron field particles is a fixed Maxwellian distribution thus enabling a steady state solution. Q is a W quasilinear operator: d / dvll(Ql df / dvll) or d / dvL(D, d f / dv,). This equation is solved by finite-differences using an alter- nating-direction-implicit algorithm described in Sauter et al. [5]. The quasi-neutral electric field Ell is calculated using a variant of the constant-particle-flux algorithm first described in Kupfer et al. [6], with the added requirement that the one-turn loop voltage due to the calculated electrostatic field is zero. Equation (1) has been solved for a range of cases: vll / vTe - 1-3, D, / Dcoll = [O. 1,101, Am$ / L = [O.  1,101, and parallel or perpendicular velocity diffusion. Dcoll is vTevee, where vTe = (Te / Figure 1 shows the time evolution of the parallel electric field for one particular case with parameters near those for the half-radius heating in DIII-D: DL / Dcoll = 1.0 inside the RF region, for velocity vll in [1,1.33]vTe, and Amfp / L = 1.0. Time z is normalized to L / vmm, vmax being the maximum velocity on the velocity grid. The length of the RF region has been taken to be 0.2 in units normalized to L.  Figure 2 gives the steady state force due to the electric field, and the pressure variation. In Fig 1, the electric field at first ( z = 0.1 1 and 0.33) evolves as one might expect: it becomes slightly positive in the RF region from Z = 0 to 0.2, giving an emf force resisting the positive flow of electrons in the RF region. In the region outside the RF, a negative electric field develops, maintaining the positive motion of the electrons. But as the electron distribution evolves towards a steady state, the electric field changes sign. Figure 2 shows the steady force FE,, due to the electric field, which further accelerates the electrons in the RF region. This force is comparable to the Ohmic force, for the case that the RF driven current density is of order the Ohmic current density. From Fig. 2, the pressure jj, normalized so that the force FF = d f ~  / dz' is in dynes, is larger than the 2 -0.0030 0.0 0.2 0.4 0.6 0.8 1.0 Normalized Distance Z FIGURE 1. Evolution of the parallel electric field. The normalized perpendicular diffusion coefficient is 1 .O and mean free path is equal to the connection length L .  Normalized Distance z FIGURE 2. Steady state electric field and normalized pressure variation. 2 GENERAL ATOMICS REPORT GA-A23 137 Harvey et al. CURRENTDRIVEDUETOLOCALIZED ELECTRON CYCLOTRON POWER DEPOSJTION IN DEI-D electric field force. It is the effective electric field 4; which accelerates electrons after they leave the RF region, thereby maintaining current continuity. In simple, near- Maxwellian cases, this will be 4; = Ell + (1 / n,e)(dp / dz) . For low collisionality, non- Maxwellian cases the effective electric field will involve an integral over velocity space giving the non-local frictional force on the electrons. The extent to which the electric force or the “pressure” force dominates has a rich dependence on the major parameters of the problem. Plots of the distribution functions versus z^ show the buildup of the non-Maxwellian distribution within the RF region, and its dissipation as a function of .? outside of the RF region. A range of simulations has been carried out and the results are shown in the following tables for parallel (lower hybrid-like) and perpendicular (EC-like) diffusion. Table 1 shows results for parallel quasilinear diffusion, for two different velocity ranges: vll/ vTe = 3-4, and VI! / vTe = 1-1.33. Several values of DL / Dcoll have been explored, and Amfp / L takes on values from 0.1 to 10.0. Current drive efficiency has been calculated for each of these cases and also for a comparable spatially uniform application of the QL diffusion with the same space-averaged diffusion coefficient. The calculated efficiencies are in good agreement with previous Fokker-Planck results, including low phase velocities. The general result from the present study is that the current drive efficiency varies very little from the uniform to the non-spatially-uniform quasilinear model, regardless of the collisionality. The largest variation between the uniform and non-uniform values is for case “rf-10” giving an 8% difference. There is negligible variation in CD efficiency when collisionality Amfp / L is varied by two orders of magnitude from 0.1 to 10. The same broad result is evident the perpendicular quasilinear diffusion results in Table 2. The CD efficiency is approximately independent of applying the quasilinear diffusion locally or globally. The reason for the independence of efficiency from collisionality is that the work done on the plasma by the effective electric field over the loop is zero: fEl;dz = 0. TABLE 1. CE Efficiency for Variations on Parallel Diffusion Designator Velocities D l  / D,u (avg) A,fp / L Local/Uniform SCD rf-8 3-4 0.002 1 .o L U If-10 0.2 L U d-14 1-1.33 0.002 L U rf-12 0.2 L U If-16 0.2 L U rf- 14-long 0.002 0.1 L rf-14-short 10.0 L 0.0459 0.0458 0.0479 0.05 15 0.0321 0.0322 0.0331 0.0324 0.0379 0.0338 0.0323 0.0320 GENERAL ATOMICS REPORT GA-A23 137 3 4 CURRENTDRTVEDUETOLOCALIZED ELJKTRON CYCLOTRON POWER DEPOSITION IN DEI-D TABLE 2. CE Efficiency for Variations on Perpendicular Diffusion Harvey et al. Designator Velocities D l  / D,,,ll (avg) Amfp / L Local/Uniform 6 c ~  rf-9 3-4 0.002 If-1 1 0.2 1f-15 1-1.33 0.002 rf-13 0.2 rf-17 0.2 0.002 1 .o L U L U L U L U L U 0.1 L 10.0 L 0.0259 0.0258 0.0264 0.0261 0.0101 0.0101 0.0099 0.0 100 0.0088 0.0096 0.0101 0.0998 The effective electric field is a combination of electrostatic and pressure forces with zero loop integral. Evidently, for the experimentally relevant parameters studied, there is small synergy between these forces and the applied RF. It is conceivable that some effects will appear at higher powers. In conclusion, we have used a 2-velocity- 1 -space-D Fokker-Planck code to calculated RF current drive efficiency for both spatially localized and uniformly applied RF power. An effective electric field was found to be the key new effect maintaining continuity of the FW induced current in current channels with Amfp I L. No substantial change in the CD efficiency from uniform RF calculations was obtained, at experimentally relevant RF power densities. This supports the use of a toroidally symmetric approximation in CQL3D. ACKNOWLEDGMENT This work was supported by the U.S. Department of Energy under Contract DE- AC03-99ER54463 and in part by the Swiss National Science Foundation. REFERENCES 1. Harvey, R.W., McCoy, M.C., “The CQL3D Fokker-Planck Code,” in Advances in Simulation and Modeling of Thermonuclear Plasmas (Proc. IAEA Technical Committee Meeting, Montreal, 1992), IAEA, Vienna (1993), p. 498. 2. Luce, T.C.,to be published in Proc. IAEA Meeting, Yokohama 1998 (IAEA, Vienna, 1999). 3. Lin-Liu, Y.R., et al., “Modeling of Electron Cyclotron Current Drive Experiments on DIII-D,” this conference. 4. Rosenbluth, M.N., etaL, Phys. Rev. 107, l(1957). 5 .  Sauter, O., et al., Contrib. Plasma Phys. 34, 169 (1994). 6. Kupfer, K., et al., Phys. Plasmas 3, 3644 (1996). GENERAL ATOMICS REPORT GA-A23 137 

Current driven due to localized electron power deposition in DIII-D

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Current driven due to localized electron power deposition in DIII-D

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